Changing B2 Visa to Permanent Visa

I am an US citizen and my fiance is currently in India. He has B1/B2 visa approved for 10 years. If I marry him in India, I understand that I need to apply for K3 visa (I-129F) and I-130 visa. I heard that nowadays it takes longer to get approved.

Instead of getting married in a foreign country, we would like to get married here in US after he comes to US using the tourist B2.

Is it possible to change his tourist visa to immigrant visa after his marriage to an US citizen? What type of visa do we need to apply to change the status? What are the chances of approval? Can he stay in the US while the visa is in process?